Close-in giant planets (e.g. ``Hot Jupiters'') are thought to form far from their host stars and migrate inward, through the terrestrial planet zone, via torques with a massive gaseous disk. Here we simulate terrestrial planet growth during and after giant planet migration. Several-Earth mass planets also form interior to the migrating Jovian planet, analogous to recently-discovered ``Hot Earths''. Very water-rich, Earth-mass planets form from surviving material outside the giant planet's orbit, often in the Habitable Zone and with low orbital eccentricities. More than a third of the known systems of giant planets may harbor Earth-like planets.
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